A polishing apparatus for polishing a substrate includes a polishing table holding a polishing pad, a top ring configured to press the substrate against the polishing pad, and first and second optical heads each configured to apply the light to the substrate and to receive reflected light from the substrate. The polishing apparatus also includes spectroscopes each configured to measure at each wavelength an intensity of the reflected light received, and a processor configured to produce a spectrum indicating a relationship between intensity and wavelength of the reflected light. The first optical head is arranged so as to face a center of the substrate, and the second optical head is arranged so as to face a peripheral portion of the substrate.